Party-list proportional representation systems are a family of voting systems emphasizing proportional representation in elections in which multiple candidates are elected (e.g., elections to parliament) through allocations to an electoral list. They can also be used as part of mixed additional member systems.
In these systems, parties make lists of candidates to be elected, and seats are distributed by elections authorities to each party in proportion to the number of votes the party receives. Voters may vote for the party, as in Albania, Argentina, Turkey, and Israel; or for candidates whose vote total will pool to the party/parties, as in Finland, Brazil and the Netherlands; or for a list of candidates, as in Hong Kong; or a choice between the last two ways stated: Luxembourg's ("panachage") and ("list vote").
Many variations on seat allocation within party-list proportional representation exist. The two most common are:
List proportional representation may also be combined in various hybrids, e.g., using the additional member system.
While the allocation formula is important, equally important is the district magnitude (number of seats in a constituency). The higher the district magnitude, the more proportional an electoral system becomes - the most proportional being when there is no division into constituencies at all and the entire country is treated as a single constituency. More, in some countries the electoral system works on two levels: at-large for parties, and in constituencies for candidates, with local party-lists seen as fractions of general, national lists. In this case, magnitude of local constituencies is irrelevant, seat apportionment being calculated at national level.
The order in which a party's list candidates get elected may be pre-determined by some method internal to the party or the candidates (a closed list system) or it may be determined by the voters at large (an open list system) or by districts (a local list system).
In a closed list systems, each political party has pre-decided who will receive the seats allocated to that party in the elections, so that the candidates positioned highest on this list tend to always get a seat in the parliament while the candidates positioned very low on the closed list will not. Voters vote only for the party, not for individual candidates.
An open list describes any variant of a party-list where voters have at least some influence on the order in which a party's candidates are elected. Open list can be anywhere from relatively closed, where a candidate can move up a predetermined list only with a certain number of votes, to completely open, where the order of the list completely depends on the number of votes each individual candidate gets.
In France, party lists in proportional elections must include as many candidates (and twice as many substitutes for the departmental elections) as there are seats to be allocated, whereas in other countries "incomplete" lists are allowed. This system of open list is known as panachage.